Submission #641653

#	Time	Username	Problem	Language	Result	Execution time	Memory
641653		Sweezy	Permutation Recovery (info1cup17_permutation)	C++17	78 / 100	4106 ms	205904 KiB

Main

#include <bits/stdc++.h>

using namespace std;
// #define int long long

#ifdef LOCAL
#include "algo/debug.h"
#else
#define debug(...) 42
#endif

using cpx = complex<double>;
const double PI = acos(-1);
vector<cpx> roots = {{0, 0}, {1, 0}};

void ensure_capacity(int min_capacity) {
    for (int len = roots.size(); len < min_capacity; len *= 2) {
        for (int i = len >> 1; i < len; i++) {
            roots.emplace_back(roots[i]);
            double angle = 2 * PI * (2 * i + 1 - len) / (len * 2);
            roots.emplace_back(cos(angle), sin(angle));
        }
    }
}

void fft(vector<cpx> &z, bool inverse) {
    int n = z.size();
    assert((n & (n - 1)) == 0);
    ensure_capacity(n);
    for (unsigned i = 1, j = 0; i < n; i++) {
        int bit = n >> 1;
        for (; j >= bit; bit >>= 1)
            j -= bit;
        j += bit;
        if (i < j)
            swap(z[i], z[j]);
    }
    for (int len = 1; len < n; len <<= 1) {
        for (int i = 0; i < n; i += len * 2) {
            for (int j = 0; j < len; j++) {
                cpx root = inverse ? conj(roots[j + len]) : roots[j + len];
                cpx u = z[i + j];
                cpx v = z[i + j + len] * root;
                z[i + j] = u + v;
                z[i + j + len] = u - v;
            }
        }
    }
    if (inverse)
        for (int i = 0; i < n; i++)
            z[i] /= n;
}

vector<int> multiply_bigint(const vector<int> &a, const vector<int> &b, int base) {
    int need = a.size() + b.size();
    int n = 1;
    while (n < need)
        n <<= 1;
    vector<cpx> p(n);
    for (size_t i = 0; i < n; i++) {
        p[i] = cpx(i < a.size() ? a[i] : 0, i < b.size() ? b[i] : 0);
    }
    fft(p, false);
    // a[w[k]] = (p[w[k]] + conj(p[w[n-k]])) / 2
    // b[w[k]] = (p[w[k]] - conj(p[w[n-k]])) / (2*i)
    vector<cpx> ab(n);
    cpx r(0, -0.25);
    for (int i = 0; i < n; i++) {
        int j = (n - i) & (n - 1);
        ab[i] = (p[i] * p[i] - conj(p[j] * p[j])) * r;
    }
    fft(ab, true);
    vector<int> result(need);
    long long carry = 0;
    for (int i = 0; i < need; i++) {
        long long d = (long long)(ab[i].real() + 0.5) + carry;
        carry = d / base;
        result[i] = d % base;
    }
    return result;
}

constexpr int digits(int base) noexcept {
    return base <= 1 ? 0 : 1 + digits(base / 10);
}

int max_len = 1;

constexpr int base = 1000000000;
constexpr int base_digits = digits(base);

constexpr int fft_base = 10000;  // fft_base^2 * n / fft_base_digits <= 10^15 for double
constexpr int fft_base_digits = digits(fft_base);

struct bigint {
    // value == 0 is represented by empty z
    vector<int> z;  // digits

    // sign == 1 <==> value >= 0
    // sign == -1 <==> value < 0
    int sign;

    bigint(long long v = 0) { *this = v; }

    bigint &operator=(long long v) {
        sign = v < 0 ? -1 : 1;
        v *= sign;
        z.clear();
        for (; v > 0; v = v / base)
            z.push_back((int)(v % base));
        return *this;
    }

    bigint(const string &s) { read(s); }

    bigint &operator+=(const bigint &other) {
        if (sign == other.sign) {
            for (int i = 0, carry = 0; i < other.z.size() || carry; ++i) {
                if (i == z.size())
                    z.push_back(0);
                z[i] += carry + (i < other.z.size() ? other.z[i] : 0);
                carry = z[i] >= base;
                if (carry)
                    z[i] -= base;
            }
        } else if (other != 0 /* prevent infinite loop */) {
            *this -= -other;
        }
        return *this;
    }

    friend bigint operator+(bigint a, const bigint &b) {
        a += b;
        return a;
    }

    bigint &operator-=(const bigint &other) {
        if (sign == other.sign) {
            if ((sign == 1 && *this >= other) || (sign == -1 && *this <= other)) {
                for (int i = 0, carry = 0; i < other.z.size() || carry; ++i) {
                    z[i] -= carry + (i < other.z.size() ? other.z[i] : 0);
                    carry = z[i] < 0;
                    if (carry)
                        z[i] += base;
                }
                trim();
            } else {
                *this = other - *this;
                this->sign = -this->sign;
            }
        } else {
            *this += -other;
        }
        return *this;
    }

    friend bigint operator-(bigint a, const bigint &b) {
        a -= b;
        return a;
    }

    bigint &operator*=(int v) {
        if (v < 0)
            sign = -sign, v = -v;
        for (int i = 0, carry = 0; i < z.size() || carry; ++i) {
            if (i == z.size())
                z.push_back(0);
            long long cur = (long long)z[i] * v + carry;
            carry = (int)(cur / base);
            z[i] = (int)(cur % base);
        }
        trim();
        return *this;
    }

    bigint operator*(int v) const { return bigint(*this) *= v; }

    friend pair<bigint, bigint> divmod(const bigint &a1, const bigint &b1) {
        int norm = base / (b1.z.back() + 1);
        bigint a = a1.abs() * norm;
        bigint b = b1.abs() * norm;
        bigint q, r;
        q.z.resize(a.z.size());

        for (int i = (int)a.z.size() - 1; i >= 0; i--) {
            r *= base;
            r += a.z[i];
            int s1 = b.z.size() < r.z.size() ? r.z[b.z.size()] : 0;
            int s2 = b.z.size() - 1 < r.z.size() ? r.z[b.z.size() - 1] : 0;
            int d = (int)(((long long)s1 * base + s2) / b.z.back());
            r -= b * d;
            while (r < 0)
                r += b, --d;
            q.z[i] = d;
        }

        q.sign = a1.sign * b1.sign;
        r.sign = a1.sign;
        q.trim();
        r.trim();
        return {q, r / norm};
    }

    friend bigint sqrt(const bigint &a1) {
        bigint a = a1;
        while (a.z.empty() || a.z.size() % 2 == 1)
            a.z.push_back(0);

        int n = a.z.size();

        int firstDigit = (int)::sqrt((double)a.z[n - 1] * base + a.z[n - 2]);
        int norm = base / (firstDigit + 1);
        a *= norm;
        a *= norm;
        while (a.z.empty() || a.z.size() % 2 == 1)
            a.z.push_back(0);

        bigint r = (long long)a.z[n - 1] * base + a.z[n - 2];
        firstDigit = (int)::sqrt((double)a.z[n - 1] * base + a.z[n - 2]);
        int q = firstDigit;
        bigint res;

        for (int j = n / 2 - 1; j >= 0; j--) {
            for (;; --q) {
                bigint r1 = (r - (res * 2 * base + q) * q) * base * base +
                            (j > 0 ? (long long)a.z[2 * j - 1] * base + a.z[2 * j - 2] : 0);
                if (r1 >= 0) {
                    r = r1;
                    break;
                }
            }
            res *= base;
            res += q;

            if (j > 0) {
                int d1 = res.z.size() + 2 < r.z.size() ? r.z[res.z.size() + 2] : 0;
                int d2 = res.z.size() + 1 < r.z.size() ? r.z[res.z.size() + 1] : 0;
                int d3 = res.z.size() < r.z.size() ? r.z[res.z.size()] : 0;
                q = (int)(((long long)d1 * base * base + (long long)d2 * base + d3) / (firstDigit * 2));
            }
        }

        res.trim();
        return res / norm;
    }

    bigint operator/(const bigint &v) const { return divmod(*this, v).first; }

    bigint operator%(const bigint &v) const { return divmod(*this, v).second; }

    bigint &operator/=(int v) {
        if (v < 0)
            sign = -sign, v = -v;
        for (int i = (int)z.size() - 1, rem = 0; i >= 0; --i) {
            long long cur = z[i] + rem * (long long)base;
            z[i] = (int)(cur / v);
            rem = (int)(cur % v);
        }
        trim();
        return *this;
    }

    bigint operator/(int v) const { return bigint(*this) /= v; }

    int operator%(int v) const {
        if (v < 0)
            v = -v;
        int m = 0;
        for (int i = (int)z.size() - 1; i >= 0; --i)
            m = (int)((z[i] + m * (long long)base) % v);
        return m * sign;
    }

    bigint &operator*=(const bigint &v) {
        *this = *this * v;
        return *this;
    }

    bigint &operator/=(const bigint &v) {
        *this = *this / v;
        return *this;
    }

    bigint &operator%=(const bigint &v) {
        *this = *this % v;
        return *this;
    }

    bool operator<(const bigint &v) const {
        if (sign != v.sign)
            return sign < v.sign;
        if (z.size() != v.z.size())
            return z.size() * sign < v.z.size() * v.sign;
        for (int i = (int)z.size() - 1; i >= 0; i--)
            if (z[i] != v.z[i])
                return z[i] * sign < v.z[i] * sign;
        return false;
    }

    bool operator>(const bigint &v) const { return v < *this; }

    bool operator<=(const bigint &v) const { return !(v < *this); }

    bool operator>=(const bigint &v) const { return !(*this < v); }

    bool operator==(const bigint &v) const { return sign == v.sign && z == v.z; }

    bool operator!=(const bigint &v) const { return !(*this == v); }

    void trim() {
        while (!z.empty() && z.back() == 0)
            z.pop_back();
        if (z.empty())
            sign = 1;
    }

    bool isZero() const { return z.empty(); }

    friend bigint operator-(bigint v) {
        if (!v.z.empty())
            v.sign = -v.sign;
        return v;
    }

    bigint abs() const { return sign == 1 ? *this : -*this; }

    long long longValue() const {
        long long res = 0;
        for (int i = (int)z.size() - 1; i >= 0; i--)
            res = res * base + z[i];
        return res * sign;
    }

    friend bigint gcd(const bigint &a, const bigint &b) { return b.isZero() ? a : gcd(b, a % b); }

    friend bigint lcm(const bigint &a, const bigint &b) { return a / gcd(a, b) * b; }

    void read(const string &s) {
        sign = 1;
        z.clear();
        int pos = 0;
        while (pos < s.size() && (s[pos] == '-' || s[pos] == '+')) {
            if (s[pos] == '-')
                sign = -sign;
            ++pos;
        }
        for (int i = (int)s.size() - 1; i >= pos; i -= base_digits) {
            int x = 0;
            for (int j = max(pos, i - base_digits + 1); j <= i; j++)
                x = x * 10 + s[j] - '0';
            z.push_back(x);
        }
        trim();
    }

    friend istream &operator>>(istream &stream, bigint &v) {
        string s;
        stream >> s;
        v.read(s);
        return stream;
    }

    friend ostream &operator<<(ostream &stream, const bigint &v) {
        if (v.sign == -1)
            stream << '-';
        stream << (v.z.empty() ? 0 : v.z.back());
        for (int i = (int)v.z.size() - 2; i >= 0; --i)
            stream << setw(base_digits) << setfill('0') << v.z[i];
        return stream;
    }

    static vector<int> convert_base(const vector<int> &a, int old_digits, int new_digits) {
        vector<long long> p(max(old_digits, new_digits) + 1);
        p[0] = 1;
        for (int i = 1; i < p.size(); i++)
            p[i] = p[i - 1] * 10;
        vector<int> res;
        long long cur = 0;
        int cur_digits = 0;
        for (int v : a) {
            cur += v * p[cur_digits];
            cur_digits += old_digits;
            while (cur_digits >= new_digits) {
                res.push_back(int(cur % p[new_digits]));
                cur /= p[new_digits];
                cur_digits -= new_digits;
            }
        }
        res.push_back((int)cur);
        while (!res.empty() && res.back() == 0)
            res.pop_back();
        return res;
    }

    bigint operator*(const bigint &v) const {
        if (min(z.size(), v.z.size()) < 150)
            return mul_simple(v);
        bigint res;
        res.sign = sign * v.sign;
        res.z = multiply_bigint(convert_base(z, base_digits, fft_base_digits),
                                convert_base(v.z, base_digits, fft_base_digits), fft_base);
        res.z = convert_base(res.z, fft_base_digits, base_digits);
        res.trim();
        return res;
    }

    bigint mul_simple(const bigint &v) const {
        bigint res;
        res.sign = sign * v.sign;
        res.z.resize(z.size() + v.z.size());
        for (int i = 0; i < z.size(); ++i)
            if (z[i])
                for (int j = 0, carry = 0; j < v.z.size() || carry; ++j) {
                    long long cur = res.z[i + j] + (long long)z[i] * (j < v.z.size() ? v.z[j] : 0) + carry;
                    carry = (int)(cur / base);
                    res.z[i + j] = (int)(cur % base);
                }
        res.trim();
        return res;
    }
};

void normalize(bigint &val) {
  while (val.z.size() > max_len) {
    val.z.pop_back();
  }
}

mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
 
struct Node {
  bigint x;
  int y;
  int id;
  bigint sum;
  Node *l, *r;
  Node(bigint val, int id) : x(val), y(rng()), id(id), sum(val), l(nullptr), r(nullptr) {
    normalize(x);
    normalize(sum);
  }
};

bigint zero = 0;

bigint& sum(Node *t) {
  return (t ? t->sum : zero);
}
 
void update(Node *t) {
  if (t == nullptr) return;
  t->sum = sum(t->l) + sum(t->r) + t->x;
  normalize(t->sum);
}

pair<Node*, Node*> split(Node *t, bigint &k) {
  if (t == nullptr) return {nullptr, nullptr};
  if (k == 0) return {nullptr, t};
  if (sum(t->l) + t->x <= k) {
    k -= sum(t->l) + t->x;
    auto [l, r] = split(t->r, k);
    t->r = l;
    update(t);
    return {t, r};
  } else {
    auto [l, r] = split(t->l, k);
    t->l = r;
    update(t);
    return {l, t};
  }
}
 
Node* merge(Node *tl, Node *tr) {
  if (tl == nullptr) return tr;
  if (tr == nullptr) return tl;
  if (tl->y > tr->y) {
    tl->r = merge(tl->r, tr);
    update(tl);
    return tl;
  } else {
    tr->l = merge(tl, tr->l);
    update(tr);
    return tr;
  }
}

void solve() {
  int n;
  cin >> n;
  vector<bigint> a(n);
  for (auto &x : a) cin >> x;

  for (int i = 1; i < n; i++) {
    bigint delta = a[i] - a[i - 1];
    max_len = max(max_len, (int) delta.z.size() + 1);
  }

  Node *root = NULL;
  root = new Node(1, 0);
  for (int i = 1; i < n; i++) {
    bigint delta = a[i] - a[i - 1];
    Node *add = new Node(delta, i);
    if (delta == 1) {
      root = merge(add, root);
    } else {
      bigint tmp = delta - 1;
      auto [l, r] = split(root, tmp);
      root = merge(l, merge(add, r));
    }
  }

  vector<int> out(n);
  function<int(Node *, int)> dfs = [&] (Node *t, int cur) {
    if (t == NULL) return 0;
    int cnt = dfs(t->l, cur);
    cur += cnt;
    out[t->id] = cur + 1;
    cur += 1;
    cnt += 1;
    cnt += dfs(t->r, cur);
    return cnt;
  };
  dfs(root, 0);

  for (auto &x : out) {
    cout << x << ' ';
  }
}

signed main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  solve();
  return 0;
}

Compilation message (stderr)

permutation.cpp: In function 'void fft(std::vector<std::complex<double> >&, bool)':
permutation.cpp:30:35: warning: comparison of integer expressions of different signedness: 'unsigned int' and 'int' [-Wsign-compare]
   30 |     for (unsigned i = 1, j = 0; i < n; i++) {
      |                                 ~~^~~
permutation.cpp:32:18: warning: comparison of integer expressions of different signedness: 'unsigned int' and 'int' [-Wsign-compare]
   32 |         for (; j >= bit; bit >>= 1)
      |                ~~^~~~~~
permutation.cpp: In function 'std::vector<int> multiply_bigint(const std::vector<int>&, const std::vector<int>&, int)':
permutation.cpp:60:26: warning: comparison of integer expressions of different signedness: 'size_t' {aka 'long unsigned int'} and 'int' [-Wsign-compare]
   60 |     for (size_t i = 0; i < n; i++) {
      |                        ~~^~~
permutation.cpp: In member function 'bigint& bigint::operator+=(const bigint&)':
permutation.cpp:118:42: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
  118 |             for (int i = 0, carry = 0; i < other.z.size() || carry; ++i) {
      |                                        ~~^~~~~~~~~~~~~~~~
permutation.cpp:119:23: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
  119 |                 if (i == z.size())
      |                     ~~^~~~~~~~~~~
permutation.cpp:121:36: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
  121 |                 z[i] += carry + (i < other.z.size() ? other.z[i] : 0);
      |                                  ~~^~~~~~~~~~~~~~~~
permutation.cpp: In member function 'bigint& bigint::operator-=(const bigint&)':
permutation.cpp:140:46: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
  140 |                 for (int i = 0, carry = 0; i < other.z.size() || carry; ++i) {
      |                                            ~~^~~~~~~~~~~~~~~~
permutation.cpp:141:40: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
  141 |                     z[i] -= carry + (i < other.z.size() ? other.z[i] : 0);
      |                                      ~~^~~~~~~~~~~~~~~~
permutation.cpp: In member function 'bigint& bigint::operator*=(int)':
permutation.cpp:165:38: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
  165 |         for (int i = 0, carry = 0; i < z.size() || carry; ++i) {
      |                                    ~~^~~~~~~~~~
permutation.cpp:166:19: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
  166 |             if (i == z.size())
      |                 ~~^~~~~~~~~~~
permutation.cpp: In member function 'void bigint::read(const string&)':
permutation.cpp:342:20: warning: comparison of integer expressions of different signedness: 'int' and 'std::__cxx11::basic_string<char>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
  342 |         while (pos < s.size() && (s[pos] == '-' || s[pos] == '+')) {
      |                ~~~~^~~~~~~~~~
permutation.cpp: In static member function 'static std::vector<int> bigint::convert_base(const std::vector<int>&, int, int)':
permutation.cpp:375:27: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<long long int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
  375 |         for (int i = 1; i < p.size(); i++)
      |                         ~~^~~~~~~~~~
permutation.cpp: In member function 'bigint bigint::mul_simple(const bigint&) const':
permutation.cpp:411:27: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
  411 |         for (int i = 0; i < z.size(); ++i)
      |                         ~~^~~~~~~~~~
permutation.cpp:413:46: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
  413 |                 for (int j = 0, carry = 0; j < v.z.size() || carry; ++j) {
      |                                            ~~^~~~~~~~~~~~
permutation.cpp:414:73: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
  414 |                     long long cur = res.z[i + j] + (long long)z[i] * (j < v.z.size() ? v.z[j] : 0) + carry;
      |                                                                       ~~^~~~~~~~~~~~
permutation.cpp: In function 'void normalize(bigint&)':
permutation.cpp:424:23: warning: comparison of integer expressions of different signedness: 'std::vector<int>::size_type' {aka 'long unsigned int'} and 'int' [-Wsign-compare]
  424 |   while (val.z.size() > max_len) {
      |          ~~~~~~~~~~~~~^~~~~~~~~

• Subtask 1: 10 / 10
• Subtask 2: 15 / 15
• Subtask 3: 18 / 18
• Subtask 4: 17 / 17
• Subtask 5: 11 / 11
• Subtask 6: 7 / 7
• Subtask 7: 0 / 16
• Subtask 8: 0 / 6